Bootstrap Equating Error
Description
These functions return bootstrap standard errors, bias, and RMSE of equating. A summary method estimates mean and weighted mean errors over the score scale.
Usage
1 2 3 4 5 6 7 8 9 10 11 12 13 14  bootstrap(x, ...)
## Default S3 method:
bootstrap(x, y, ...)
## S3 method for class 'equate'
bootstrap(x, xp = x$x, yp = x$y, ...)
## S3 method for class 'freqtab'
bootstrap(x, y, xn = sum(x), yn = sum(y), reps = 100,
crit, args, eqs = FALSE, ...)
## S3 method for class 'bootstrap'
summary(object, weights, subset, ...)

Arguments
x 
either an equating object, obtained with the 
y 
score distribution of class “ 
xp, yp 
optional frequency tables replacing those equated in 
xn, yn 
integers specifying the number of scores to sample from each distribution at each replication (default is the total number observed in each). 
reps 
number of bootstrap replications. 
crit 
vector of equated scores serving as the criterion equating
function when calculating bootstrap bias and RMSE, both of which are
returned when 
args 
named list of equating arguments, passed to

eqs 
logical, with default 
object 

weights 
vector of weights to be used in calculating weighted average
errors with 
subset 
vector indicating a subset of the score scale for which errors should be summarized. 
... 
further arguments passed to or from other methods. 
Details
Samples are drawn of size xn
and yn
, with replacement, from
each score distribution. Form Y equivalents of each form X score are then
obtained using either the arguments in the equating output or those
provided. This process is repeated reps
times. Standard errors are
calculated as standard deviations over replications for each score point;
bias is the mean equated score over replications, minus the criterion; and
RMSE is the square root of the squared standard error and squared bias
combined.
The bootstrap method for objects of class “equate
” is designed
to be called from within equate
. It simply extracts the
necessary arguments from the equating output before bootstrapping.
When each element in args
is a named list of equating arguments,
multiple equatings are performed at each replication in the bootstrapping.
The summary method returns a data.frame
of mean standard errors,
bias, and rmse, and weighted and absolute means, as applicable.
Value
With bootstrap
, a list is returned, containing arguments
supplied for x
, y
, reps
, xn
, yn
, and
args
. For a single equating, the mean
equating function over
replications and a vector of standard errors se
are included,
along with vectors of bias
and rmse
, when crit
is
provided, and a matrix of equating functions eqs
when
eqs = TRUE
. For multiple equatings, where each element of
args
is a list of equating arguments, matrices are returned for the
mean functions, standard error, bias, and RMSE, and the equating functions
will be returned as a list of matrices. The summary
method returns a
data frame of mean standard errors, bias, and rmse, and weighted and
absolute means, as applicable.
Methods (by class)

default
: Default boostrap method for “freqtab
” objects. 
equate
: Method for “equate
” objects. 
freqtab
: Bootstrap method for “freqtab
” objects.
Author(s)
Anthony Albano tony.d.albano@gmail.com
See Also
plot.bootstrap
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20  # Parametric bootstrapping using smoothed
# frequency distributions
set.seed(111213)
x < freqtab(KBneat$x, scales = list(0:36, 0:12))
y < freqtab(KBneat$y, scales = list(0:36, 0:12))
xp < loglinear(x, asfreqtab = TRUE)
yp < loglinear(y, asfreqtab = TRUE)
crit < equate(xp, yp, "e", "c")$conc$yx
eqargs < list(m.t = list(type = "m", method = "t"),
l.t = list(type = "l", method = "t"))
bootout1 < bootstrap(x = x, y = y, xn = 20, yn = 20,
crit = crit, args = eqargs, reps = 30)
plot(bootout1, out = "rmse", legendplace = "top",
addident = FALSE)
# Bootstraps for an existing equating
eq < equate(x, y, type = "m", method = "t")
bootout2 < bootstrap(eq, xn = 100, yn = 100,
crit = crit, reps = 20)
summary(bootout2)
